Abstract: Logic is the rule of rational thinking. When thinking is expressed in language, logic becomes the rule of language. Logic is not the law of objective things, each discipline studies different laws, while logic is applicable to all disciplines because all disciplines use rational thought and language. Logical judgment is not necessarily the truth. In the subjective world, the simple atomic concepts can never change. In the objective world, concrete things are complicated, so A can be different from A. The rules of formal logic, such as the law of identity, the law of exclusion of middle and the law of non-contradiction, are the rules of the subjective world, and are the methods to deal with the logical structures in the subjective world, rather than the methods to deal with the real things in the objective world. The understanding of any objective thing requires a process from simple to complex. In the beginning stage of cognition, we must simplify and abstract complex objects, and use formal logic when simplifying and abstracting. For example, suppose that the Chaobai River this year is the same river as the Chaobai River in the past ten years, and then use the hydrological data of the past ten years to predict the situation of the river this year. This hypothesis is simple and useful but not objectively true. Making objective things obey the rules of formal logic is entirely artificial. Because only by following these rules can we derive useful conclusions. The purpose of simplification is to make the sentences do not contain contradictions, easy to thinking and calculation. The actual objective things contain contradictions and do not conform to formal logic. So dialectical logic negates the rules of formal logic.
Key words: Logic philosophy; Formal logic; Dialectical logic; Useful; Objectivity